Model 3 analysis
Benjamin Mercier
Last updated on 13 October, 2022
Model 3
Description of the model
This third model is again a slight variant of the two first, in which we assign a specific \(\alpha\) to each predator, but we also divide it by the degree of the predator (number of preys). In doing so, we can still isolate difference between predator, to check if some predator seems to be different from the whole, but also try to divide between each of ones predators prey. \[\begin{align}
F_{ij}^{real} &= \frac{\alpha_{j}}{D_{j}} * B_i * \frac{B_j}{M_j}
\end{align}\]
This model was fit with a hierarchy implemented on the alpha parameter. A global alpha was estimated, with 118 respective unique alphas for each predators. In contrast with model 2, the alphas in model 3 are divided by the predator’s degree.
Summary table
| mean | se_mean | sd | 2.5% | 25% | 50% | 75% | 97.5% | n_eff | Rhat | |
|---|---|---|---|---|---|---|---|---|---|---|
| a_pop | -10.020670 | 0.0153252 | 0.3601779 | -10.735072 | -10.268143 | -10.016719 | -9.775512 | -9.322804 | 552.3597 | 1.0070492 |
| a_sd | 3.847411 | 0.0019136 | 0.2664588 | 3.362061 | 3.664654 | 3.833639 | 4.016568 | 4.406197 | 19388.7332 | 0.9999259 |
| sigma | 1.679814 | 0.0003024 | 0.0410108 | 1.601866 | 1.651454 | 1.678931 | 1.706225 | 1.763753 | 18389.1117 | 0.9999737 |
Exploring parameters posterior distribution
General parameters
Respective predator alphas
Rhats
Examining Rhats to see if all parameters have converge
Simulated data vs observed data
